Teak Veneer Loss Solution?  

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Attached right here.

I'd say you were in luck -- because the damage is limited to the end of an edgeband, not a full side panel.  The remaining veneer can be removed from that piece, and a new piece of veneer edgebanding applied, without impacting the rest of the piece.
This will be the necessary step; you wouldn't want to settle for replacing just the missing end of the veneer, as no good match would be possible with the new material, and the repair wouldn't be much better than the present damage. (It will be neccesary to choose carefully when shopping for the new edge tape; don't settle for the first roll off the rack, but seek to match the existing material on the cabinet.  The color may be lighter; this can be corrected.  Don't buy material which is darker, or whose grain is too different from the existing.)
First, try heat; many manufacturers use edgebanding machines which apply hot parrafin-based adhesive to the edge of a panel and immediately apply a strip of veneer to the glued edge, pressing it in place and subsequently trimming the excess width and length before the panel leaves the machine.  For repairs like this, we want edge tape with the glue already applied. Glue-backed veneer edge tape is available at lumber dealers servicing the cabinetmaking trade.  A small roll of teak edge tape might even show up at a good hardware shop.
You will be able to apply this tape with a kitchen iron or a heat gun; a hair dryer may work. We'll go over the methods for removing the excess tape and finishing the repair. Experiment with a scrap of the tape, on a piece of scrap wood, to gain experience.
Use the iron on medium setting, or the hairdryer set on high, to remove the existing edgeband. A panel of scrap material placed over the adjacent surface might be a good precaution against overheating the finish on the cabinet.  Clamp the panel so it guides the tool over the adgeband only. Start at one end and apply heat to raise a corner of the tape.  Once an edge of the existing tape can be lifted, grab it with pliers and pull gently but firmly as you apply heat in a consistent and linear fashion -- just as a machine might do it.  Then reheat the bare edge and, using a putty knife, follow the heat with the knife (again in a machine-like continuous progression) and scrape the bulk of any remaining glue.  A small and even remaining glue residue will do no harm. Paint thinner (mineral spirits) will remove glue from your tools, and will not damage the cabinet finish.
Let's pause here; shop for edgetape, and try removing the veneer as described. If heat does not soften the glue, we'll have to explore other options for removing the edge band.  

Adminiatrators, do you want to move this thread to the Repair department ?